39edt

The 39 equal division of 3, the tritave, divides it into 39 equal parts of 48.678 cents each, a nonoctave tuning corresponding to 24.606 edo. It is a strong no-twos 13-limit system, a fact first noted by Paul Erlich, and like 26edt and 52edt it is a multiple of 13edt and so contains the Bohlen-Pierce scale. It is contorted in the 7-limit, tempering out the same BP commas 245/243 and 3125/3087 as 13edt. In the 11-limit it tempers out 1331/1323 and in the 13-limit 275/273, 847/845 and 1575/1573. It is related to the 49f&172f temperament tempering out 245/243, 275/273, 847/845 and 1575/1573, which has map [<1 0 0 0 0 0|, <0 39 57 69 85 91|]. This has a POTE generator which is an approximate 77/75 of 48.822 cents. 39edt is the ninth no-twos zeta peak edt.

Intervals of 39EDT

Degrees of 39EDT	Cents Value	¢ Octave-Reduced	Degrees of BP	Comments
0	0.000		0	1/1
1	48.768			39th root of 3
2	97.536
3	146.304		1	13th root of 3
4	195.072
5	243.840
6	292.608		2
7	341.377
8	390.145
9	438.913		3
10	487.681
11	536.449
12	585.217		4
13	633.985			cube root of 3
14	682.753
15	731.521		5
16	780.289
17	829.057
18	877.825		6
19	926.593
20	975.362
21	1024.130		7
22	1072.898
23	1121.666
24	1170.434		8
25	1219.202	19.202
26	1267.970	67.970
27	1316.738	116.738	9
28	1365.506	165.506
29	1414.274	214.274
30	1463.042	263.042	10
31	1511.810	311.810
32	1560.578	360.578
33	1609.347	409.347	11
34	1658.115	458.115
35	1706.883	506.883
36	1755.651	555.651	12
37	1804.419	604.419
38	1853.187	653.187
39	1901.955	701.955	13	3/1 (tritave)
40	1950.723	750.723
41	1999.491	799.491
42	2048.259	848.259	14
43	2097.027	897.027
44	2145.795	945.795
45	2194.563	994.563	15
46	2243.332	1043.332
47	2292.100	1092.100
48	2340.868	1140.868	16
49	2389.636	1189.636
50	2438.404	38.404
51	2487.172	87.172	17
52	2535.940	135.940
53	2584.708	184.708
54	2633.476	233.476	18
55	2682.244	282.244
56	2731.012	331.012
57	2779.780	379.780	19
58	2828.548	428.548
59	2877.317	477.317
60	2926.085	526.085	20
61	2974.853	574.853
62	3023.621	623.621
63	3072.389	672.389	21
64	3121.157	721.157
65	3169.925	769.925
66	3218.693	818.693	22
67	3267.461	867.461
68	3316.229	916.229
69	3364.997	964.997	23
70	3413.765	1013.765
71	3462.533	1062.533
72	3511.302	1111.302	24
73	3560.070	1160.070
74	3608.838	8.838
75	3657.606	57.606	25
76	3706.374	106.374
77	3755.142	155.142
78	3803.910	203.910	26	9/1